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Properties

Label 25.32
Level 25
Weight 32
Dimension 705
Nonzero newspaces 4
Sturm bound 1600
Trace bound 1

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 32 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(1600\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{32}(\Gamma_1(25))\).

Total New Old
Modular forms 789 726 63
Cusp forms 761 705 56
Eisenstein series 28 21 7

Trace form

\( 705 q - 25582 q^{2} + 73744966 q^{3} - 4669916610 q^{4} + 18767592685 q^{5} - 1000468662290 q^{6} - 27445366630522 q^{7} - 357659573960410 q^{8} - 4064494113293610 q^{9} + O(q^{10}) \) \( 705 q - 25582 q^{2} + 73744966 q^{3} - 4669916610 q^{4} + 18767592685 q^{5} - 1000468662290 q^{6} - 27445366630522 q^{7} - 357659573960410 q^{8} - 4064494113293610 q^{9} + 386901086661360 q^{10} + 42161662559653710 q^{11} + 282160536548453238 q^{12} - 586952384909014274 q^{13} + 1599382161501229190 q^{14} + 5427645227072985330 q^{15} - 89968803511162470770 q^{16} + 42733720285390966228 q^{17} + 411722268366634995106 q^{18} - 181413093429290895630 q^{19} + 326606659127270955290 q^{20} - 1422081671391163996230 q^{21} + 1527531936178016847846 q^{22} - 4992623681566637667774 q^{23} + 39139352188973393999020 q^{24} - 29913473419605201410565 q^{25} + 56876522576324445165900 q^{26} - 49623287422866261614720 q^{27} + 127570232003012710088534 q^{28} - 301481039138398599786030 q^{29} + 521143448842537379992390 q^{30} - 650616505472112098738230 q^{31} + 602002331214522017656758 q^{32} + 658348110334848643435842 q^{33} - 2723769675000792572689810 q^{34} + 5275342367095770748348100 q^{35} - 17734924428021043362220170 q^{36} + 2222197007695923405175103 q^{37} - 8510108563965664056679300 q^{38} - 73457588814445694623367250 q^{39} + 90278626552823891504630540 q^{40} - 54212325127959255530874590 q^{41} + 30946462313988485981125306 q^{42} + 48932009426856011095377086 q^{43} - 174811984744954171046951480 q^{44} - 315349135961035476163064275 q^{45} + 268699663655318731776230090 q^{46} - 444775326415630223558301122 q^{47} + 1091925187384437070214648916 q^{48} - 909871557070280628278105015 q^{49} - 518392813728829024577458750 q^{50} - 1848915160385040176218450920 q^{51} + 4802736017757111591629135908 q^{52} - 1980577724779075446251488969 q^{53} - 2521266427782394013475442240 q^{54} + 3596082600807220490524820090 q^{55} - 3144661382011044288143762030 q^{56} + 7640596514509199279314927430 q^{57} + 5589653206118955206494370980 q^{58} - 16992643586170314261044434260 q^{59} + 245735927437604227024959170 q^{60} + 11310139920193226171583913470 q^{61} + 1896615590805750717763048416 q^{62} - 60197889584716285004323072444 q^{63} + 78189774092749593505696992280 q^{64} + 67769523010397385882511480775 q^{65} - 51795410620831867870730587090 q^{66} + 104004008827024103955696767518 q^{67} + 128087970674724687683273117414 q^{68} - 219339932000614805479448365280 q^{69} + 181120776197681528577640977630 q^{70} + 112793093533962622637686791110 q^{71} - 939822734463308086892318076360 q^{72} - 163488438349376307520863113034 q^{73} + 1127282661207515745911504222580 q^{74} - 164084918609198473753808369390 q^{75} - 1159795076034795271557190817980 q^{76} + 1339531912158227317710530921286 q^{77} + 4476220328923023703041097191272 q^{78} - 4456330922270249872612823544850 q^{79} + 195871562558472880382995993670 q^{80} - 1731062104020059948291775842070 q^{81} + 59576682888497227161869871126 q^{82} - 3986935266414247391604779180784 q^{83} + 6288850219005618237544052074790 q^{84} + 2013928709568906548446999984895 q^{85} - 3234267189987804645598814865030 q^{86} - 841006173180524884813988388820 q^{87} + 15849694990852697610780645814590 q^{88} - 11274900732822611015148701261385 q^{89} - 19338345198089667215394202290930 q^{90} + 11807173886171997674229863921210 q^{91} + 48503297885632062845131038656418 q^{92} - 56442688381548629948274257958668 q^{93} + 25536782441526373438109112708230 q^{94} + 38382414290414567051879702035210 q^{95} + 8073814037779014378452348062250 q^{96} - 79564078273684745384641031872022 q^{97} + 18956353247263787593186029487294 q^{98} + 120437838105050690069055250339860 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{32}^{\mathrm{new}}(\Gamma_1(25))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
25.32.a \(\chi_{25}(1, \cdot)\) 25.32.a.a 2 1
25.32.a.b 5
25.32.a.c 6
25.32.a.d 10
25.32.a.e 10
25.32.a.f 14
25.32.b \(\chi_{25}(24, \cdot)\) 25.32.b.a 4 1
25.32.b.b 10
25.32.b.c 12
25.32.b.d 20
25.32.d \(\chi_{25}(6, \cdot)\) n/a 308 4
25.32.e \(\chi_{25}(4, \cdot)\) n/a 304 4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{32}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{32}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{32}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{32}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)